Here is a brief list of the vie ferrate I have completed or would like to do in various areas I have visited, with those I have completed marked with the date(s).

Genoa

The main ferrata close to Genoa and other areas I often visit because of friends is:

There are a few other ferrate nearby, though they are about two hours away by car from Genoa and therefore require significantly more effort to reach:

Falesie

To properly go climbing in Genoa, I found ZenaClimbing, which provides an excellent listing. There is also this guide.